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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

Efremova, L. S., and E. N. Makhrova. "One-dimensional dynamical systems." Russian Mathematical Surveys 76, no. 5 (October 1, 2021): 821–81. http://dx.doi.org/10.1070/rm9998.

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Abstract The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological entropy are investigated. Necessary and sufficient conditions for entropy chaos in continuous maps of an interval, a circle, or a finite graph, and sufficient conditions for entropy chaos in continuous maps of dendrites are presented. Reasons for similarities and differences between the properties of maps defined on the continua under consideration are analyzed. Extensions of Sharkovsky’s theorem to certain discontinuous maps of a line or an interval and continuous maps on a plane are considered. Bibliography: 207 titles.

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2

Li, Denghui, Zhenbang Cao, Xiaoming Zhang, Celso Grebogi, and Jianhua Xie. "Strange Nonchaotic Attractors From a Family of Quasiperiodically Forced Piecewise Linear Maps." International Journal of Bifurcation and Chaos 31, no. 07 (June 15, 2021): 2150111. http://dx.doi.org/10.1142/s021812742150111x.

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In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

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3

Scott, C. B., and Eric Mjolsness. "Graph diffusion distance: Properties and efficient computation." PLOS ONE 16, no. 4 (April 27, 2021): e0249624. http://dx.doi.org/10.1371/journal.pone.0249624.

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We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite “graph limits” by means of Cauchy sequences of graphs related to one another by our distance measure.

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4

ANDRES, JAN, PAVLA ŠNYRYCHOVÁ та PIOTR SZUCA. "SHARKOVSKII'S THEOREM FOR CONNECTIVITY Gδ-RELATIONS". International Journal of Bifurcation and Chaos 16, № 08 (серпень 2006): 2377–93. http://dx.doi.org/10.1142/s0218127406016136.

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A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity Gδ-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity Gδ-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.

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5

Margielewicz, J., J. Wojnarowski, and S. Zawiślak. "Numerical Studies of Nonlinear Gearing Models Using Bond Graph Method." International Journal of Applied Mechanics and Engineering 23, no. 4 (November 1, 2018): 885–96. http://dx.doi.org/10.2478/ijame-2018-0049.

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Abstract The present paper is dedicated to computer simulations performed using a numerical model of a one-stage gear. The motion equations were derived utilizing the bond graph method. The formulated model takes into consideration the variable stiffness of toothings as well as an inter-tooth clearance which has been represented via discontinuous elements with so called dead zones. As a result of these assumptions, the nonlinear model was obtained which enables representation of the dynamic phenomena of the considered gear. In the paper, an influence of errors of gear wheels’ co-operation on the character of excited dynamic phenomena was studied. The methodology of the analyses consists in utilization of the following tools: color maps of distribution of the maximal Lapunov coefficient and bifurcation diagrams. Based upon them, the parameters were determined, for which the Poincare portrait represents a structure of the chaotic attractor. For the identified attractors, the initial attractors were calculated numerically - which along with the changes of the control parameters are subjected to multiplication, stretching or rotation.

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6

Bellettini, Giovanni, Alaa Elshorbagy, Maurizio Paolini, and Riccardo Scala. "On the relaxed area of the graph of discontinuous maps from the plane to the plane taking three values with no symmetry assumptions." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 2 (July 9, 2019): 445–77. http://dx.doi.org/10.1007/s10231-019-00887-0.

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7

Abello, James. "Hierarchical graph maps." Computers & Graphics 28, no. 3 (June 2004): 345–59. http://dx.doi.org/10.1016/j.cag.2004.03.012.

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8

Bazhenov, Viktor, Olha Pogorelova, and Tetiana Postnikova. "Transient Chaos in Platform-vibrator with Shock." Strength of Materials and Theory of Structures, no. 106 (May 24, 2021): 22–40. http://dx.doi.org/10.32347/2410-2547.2021.106.22-40.

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Анотація:

Platform-vibrator with shock is widely used in the construction industry for compacting and molding large concrete products. Its mathematical model, created in our previous work, meets all the basic requirements of shock-vibration technology for the precast concrete production on low-frequency resonant platform-vibrators. This model corresponds to the two-body 2-DOF vibro-impact system with a soft impact. It is strongly nonlinear non-smooth discontinuous system. This is unusual vibro-impact system due to its specific properties. The upper body, with a very large mass, breaks away from the lower body a very short distance, and then falls down onto the soft constraint that causes a soft impact. Then it bounces and falls again, and so on. A soft impact is simulated with nonlinear Hertzian contact force. This model exhibited many unique phenomena inherent in nonlinear non-smooth dynamical systems with varying control parameters. In this paper, we demonstrate the transient chaos in a vibro-impact system. Our finding of transient chaos in platform-vibrator with shock, besides being a remarkable phenomenon by itself, provides an understanding of the dynamical processes that occur in the platform-vibrator when varying the technological mass of the mold with concrete. Phase trajectories, Poincaré maps, graphs of time series and contact forces, Fourier spectra, the largest Lyapunov exponent, and wavelet characteristics are used in numerical investigations to determine the chaotic and periodic phases of the realization. We show both the dependence of the transient chaos on the control parameter value and the sensitive dependence on the initial conditions. We hope that this analysis can help avoid undesirable platform-vibrator behaviour during design and operation due to inappropriate system parameters, since transient chaos may be a dangerous and unwanted state of a vibro-impact system.

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9

Bischi, Gian-Italo, Laura Gardini, and Fabio Tramontana. "Bifurcation curves in discontinuous maps." Discrete & Continuous Dynamical Systems - B 13, no. 2 (2010): 249–67. http://dx.doi.org/10.3934/dcdsb.2010.13.249.

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10

Pavlovic, Branka. "Discontinuous Maps from Lipschitz Algebras." Journal of Functional Analysis 155, no. 2 (June 1998): 436–54. http://dx.doi.org/10.1006/jfan.1997.3232.

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11

Tan, Raymond R., Kathleen B. Aviso, Angelyn R. Lao, and Michael Angelo B. Promentilla. "P-graph Causality Maps." Process Integration and Optimization for Sustainability 5, no. 3 (January 12, 2021): 319–34. http://dx.doi.org/10.1007/s41660-020-00147-2.

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12

MAI, JIE-HUA. "Pointwise-recurrent graph maps." Ergodic Theory and Dynamical Systems 25, no. 2 (April 2005): 629–37. http://dx.doi.org/10.1017/s0143385704000720.

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13

KOLLÁR, LÁSZLÓ E., GÁBOR STÉPÁN, and JÁNOS TURI. "DYNAMICS OF PIECEWISE LINEAR DISCONTINUOUS MAPS." International Journal of Bifurcation and Chaos 14, no. 07 (July 2004): 2341–51. http://dx.doi.org/10.1142/s0218127404010837.

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In this paper, the dynamics of maps representing classes of controlled sampled systems with backlash are examined. First, a bilinear one-dimensional map is considered, and the analysis shows that, depending on the value of the control parameter, all orbits originating in an attractive set are either periodic or dense on the attractor. Moreover, the dense orbits have sensitive dependence on initial data, but behave rather regularly, i.e. they have quasiperiodic subsequences and the Lyapunov exponent of every orbit is zero. The inclusion of a second parameter, the processing delay, in the model leads to a piecewise linear two-dimensional map. The dynamics of this map are studied using numerical simulations which indicate similar behavior as in the one-dimensional case.

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14

Rivière, Tristan. "Everywhere discontinuous harmonic maps into spheres." Acta Mathematica 175, no. 2 (1995): 197–226. http://dx.doi.org/10.1007/bf02393305.

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15

J. AbdulHussein, Hussein. "Some Chaos on Graph Maps." Muthanna Journal of Pure Science 4, no. 2 (October 19, 2017): 15–19. http://dx.doi.org/10.18081/2226-3284/017-10/15-19.

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16

AbdulHussein, Hussein J., and Akram B. Attar. ""Some Chaos on Graph Maps"." Muthanna Journal of Pure Science 4, no. 2 (October 19, 2017): 15–19. http://dx.doi.org/10.52113/2/04.02.2017/15-19.

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Анотація:

"Let be a graph and be continuous function, we study some types of chaotic functions on a graph and find the relation between them. We also introduce a new type of chaos defined on a graph called strongly chaotic and characterization generically chaotic and densely chaotic on graph maps."

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17

Yokoi, Katsuya. "Strong Transitivity and Graph Maps." Bulletin of the Polish Academy of Sciences Mathematics 53, no. 4 (2005): 377–88. http://dx.doi.org/10.4064/ba53-4-3.

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18

KELLY, MICHAEL R. "Graph representatives for surface maps." Ergodic Theory and Dynamical Systems 27, no. 03 (April 17, 2007): 849. http://dx.doi.org/10.1017/s0143385706000964.

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19

Heath, L. S. "Graph embeddings and simplicial maps." Theory of Computing Systems 30, no. 1 (February 1997): 51–65. http://dx.doi.org/10.1007/bf02679453.

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20

Fedeli, Alessandro. "On discontinuous transitive maps and dense orbits." Bulletin of the Belgian Mathematical Society - Simon Stevin 13, no. 2 (June 2006): 241–45. http://dx.doi.org/10.36045/bbms/1148059460.

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21

Avrutin, Viktor, and Mike R. Jeffrey. "Bifurcations of hidden orbits in discontinuous maps." Nonlinearity 34, no. 9 (July 26, 2021): 6140–72. http://dx.doi.org/10.1088/1361-6544/ac12ac.

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22

Bauer, M., S. Habip, D. R. He, and W. Martienssen. "New type of intermittency in discontinuous maps." Physical Review Letters 68, no. 11 (March 16, 1992): 1625–28. http://dx.doi.org/10.1103/physrevlett.68.1625.

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23

De Sousa Mendes, Miguel Ângelo. "Discontinuous maps exhibiting symmetry Lebesgue-almost everywhere." Dynamical Systems 21, no. 3 (September 2006): 337–50. http://dx.doi.org/10.1080/14689360600553058.

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24

Fu, Xin-Chu, Zhan-He Chen, Hongjun Gao, Chang-Pin Li, and Zeng-Rong Liu. "Chaotic sets of continuous and discontinuous maps." Nonlinear Analysis: Theory, Methods & Applications 72, no. 1 (January 2010): 399–408. http://dx.doi.org/10.1016/j.na.2009.06.075.

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25

Shahzad, N. "Random fixed points of discontinuous random maps." Mathematical and Computer Modelling 41, no. 13 (June 2005): 1431–36. http://dx.doi.org/10.1016/j.mcm.2004.02.036.

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26

Farago, Oded, and Yacov Kantor. "Pseudo-boundaries in discontinuous two-dimensional maps." Journal of Physics A: Mathematical and General 31, no. 2 (January 16, 1998): 445–51. http://dx.doi.org/10.1088/0305-4470/31/2/006.

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27

Bressloff, P. C., and J. Stark. "Neuronal dynamics based on discontinuous circle maps." Physics Letters A 150, no. 3-4 (November 1990): 187–95. http://dx.doi.org/10.1016/0375-9601(90)90119-9.

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28

Atkinson, Scott. "Graph products of completely positive maps." Journal of Operator Theory 81, no. 1 (December 15, 2018): 133–56. http://dx.doi.org/10.7900/jot.2017dec13.2177.

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Анотація:

We define the graph product of unital completely positive maps on a universal graph product of unital C∗-algebras and show that it is unital completely positive itself. To accomplish this, we introduce the notion of the non-commutative length of a word, and we obtain a Stinespring construction for concatenation. This result yields the following consequences. The graph product of positive-definite functions is positive-definite. A graph product version of von Neumann's inequality holds. Graph independent contractions on a Hilbert space simultaneously dilate to graph independent unitaries.

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29

Thurston, Hugh. "Can a Graph Be Both Continuous and Discontinuous?" American Mathematical Monthly 96, no. 9 (November 1989): 814. http://dx.doi.org/10.2307/2324843.

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30

Thurston, Hugh. "Can a Graph Be Both Continuous and Discontinuous?" American Mathematical Monthly 96, no. 9 (November 1989): 814–15. http://dx.doi.org/10.1080/00029890.1989.11972285.

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31

Valiente, Gabriel. "Adjacency Maps and Efficient Graph Algorithms." Algorithms 15, no. 2 (February 20, 2022): 67. http://dx.doi.org/10.3390/a15020067.

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Анотація:

Graph algorithms that test adjacencies are usually implemented with an adjacency-matrix representation because the adjacency test takes constant time with adjacency matrices, but it takes linear time in the degree of the vertices with adjacency lists. In this article, we review the adjacency-map representation, which supports adjacency tests in constant expected time, and we show that graph algorithms run faster with adjacency maps than with adjacency lists by a small constant factor if they do not test adjacencies and by one or two orders of magnitude if they perform adjacency tests.

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32

MIYAZAWA, Megumi. "Chaos and Entropy for Graph Maps." Tokyo Journal of Mathematics 27, no. 1 (June 2004): 221–25. http://dx.doi.org/10.3836/tjm/1244208486.

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33

Hu, Jingtian, and Andrew L. Ferguson. "Global graph matching using diffusion maps." Intelligent Data Analysis 20, no. 3 (April 20, 2016): 637–54. http://dx.doi.org/10.3233/ida-160824.

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34

Llibre, Jaume, and Michał Misiurewicz. "Negative periodic orbits for graph maps." Nonlinearity 19, no. 3 (February 6, 2006): 741–46. http://dx.doi.org/10.1088/0951-7715/19/3/011.

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35

Blokh, Alexander, and Michał Misiurewicz. "Attractors for graph critical rational maps." Transactions of the American Mathematical Society 354, no. 9 (April 30, 2002): 3639–61. http://dx.doi.org/10.1090/s0002-9947-02-02999-9.

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36

Ramos, C. Correia, Nuno Martins, and Paulo R. Pinto. "On graph algebras from interval maps." Annals of Functional Analysis 10, no. 2 (May 2019): 203–17. http://dx.doi.org/10.1215/20088752-2018-0019.

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37

Dessmark, Anders, and Andrzej Pelc. "Optimal graph exploration without good maps." Theoretical Computer Science 326, no. 1-3 (October 2004): 343–62. http://dx.doi.org/10.1016/j.tcs.2004.07.031.

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38

Mai, Jie-Hua, and Song Shao. "R¯=R∪P¯ for graph maps." Journal of Mathematical Analysis and Applications 350, no. 1 (February 2009): 9–11. http://dx.doi.org/10.1016/j.jmaa.2008.09.006.

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39

Whittington, Keith. "The graph spaces of connectivity maps." Topology and its Applications 68, no. 2 (February 1996): 97–105. http://dx.doi.org/10.1016/0166-8641(95)00060-7.

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40

HongJian, XI, and SUN TaiXiang. "Negative limit sets of graph maps." SCIENTIA SINICA Mathematica 47, no. 5 (November 14, 2016): 591–98. http://dx.doi.org/10.1360/scm-2016-0259.

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41

Kwak, Jin Ho, and Young Soo Kwon. "Unoriented Cayley maps." Studia Scientiarum Mathematicarum Hungarica 43, no. 2 (June 1, 2006): 137–57. http://dx.doi.org/10.1556/sscmath.43.2006.2.1.

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A Cayley map is an embedding of a Cayley graph into an orientable surface and it has been studied intensively for last decades [1, 8, 10, 11, 15, 16, 17, 18, etc]. In this paper we consider an embedding of a Cayley graph into an orientable or nonorientable surface. We call it a generalized Cayley map. We describe the automorphism group of a generalized Cayley map and determine when a generalized Cayley map can be regular. The Petrie dual of a generalized Cayley map is also studied. Finally, the first infinite family of graphs which can be underlying graphs of nonorientable regular maps is presented.

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42

Yang, Yunfeng, and Xue Bai. "Synchronization time in two coupled cluster networks based on discontinuous map." Journal of Physics: Conference Series 2313, no. 1 (July 1, 2022): 012013. http://dx.doi.org/10.1088/1742-6596/2313/1/012013.

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Анотація:

Abstract The synchronization time in the coupled discontinuous maps is investigated. The results show that the synchronization time of the coupled discontinuous systems exhibits a non-monotonic behaviour as the coupling strength increases. Moreover, a coexistence attractor, which consists of a period state and synchronization one, is found, and it exhibits a riddle basin character. The initial conditions of coupled systems, which is close to the basin boundary of period attractor, can lead to a long quasiperiodic transient, and the trajectory jumps from one region to another one in the phase space. Finally, the non-monotonic behaviour of the synchronization time of the coupled discontinuous systems is also checked in other types of discontinuous maps.

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43

Łucjan, Kamila, and Paweł Wojtanowicz. "Continuous or discontinuous? Empirical study on animated maps." Polish Cartographical Review 50, no. 3 (September 1, 2018): 127–40. http://dx.doi.org/10.2478/pcr-2018-0008.

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Анотація:

Abstract Advancements in computer technology that have occurred in recent decades have enabled an intensive development in cartographic methods for direct representation of phenomena dynamics. Even with the appearance of ever more advanced technical solutions, the theoretical basis still needs supplementing. The previous cartographic literature emphasises the importance of congruence and isomorphism principles preservation that aims at increasing the effectiveness of dynamic displays. Nevertheless, it is frequently the case that discontinuous phenomena are depicted with the use of smooth transitions. For this reason, it is vital that experimental research should lead to defining which representation methods are appropriate for a given type of content. Our study was focused on the cartographic design of scene transitions in animated maps. Two main conclusions of the research indicate that 1) mode of transition influences the interpretation of the content of cartographic animation depicting discrete changes, 2) maps executed in a smooth mode demonstrate lower effectiveness when compared with animations using an abrupt and abrupt with decay effect transitions.

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44

Wackerbauer, Renate. "Noise-induced stabilization of one-dimensional discontinuous maps." Physical Review E 58, no. 3 (September 1, 1998): 3036–44. http://dx.doi.org/10.1103/physreve.58.3036.

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45

Markus, Mario. "Chaos in Maps with Continuous and Discontinuous Maxima." Computers in Physics 4, no. 5 (1990): 481. http://dx.doi.org/10.1063/1.4822940.

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46

JAIN, PARAG, and SOUMITRO BANERJEE. "BORDER-COLLISION BIFURCATIONS IN ONE-DIMENSIONAL DISCONTINUOUS MAPS." International Journal of Bifurcation and Chaos 13, no. 11 (November 2003): 3341–51. http://dx.doi.org/10.1142/s0218127403008533.

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Анотація:

We present a classification of border-collision bifurcations in one-dimensional discontinuous maps depending on the parameters of the piecewise linear approximation in the neighborhood of the point of discontinuity. For each range of parameter values we derive the condition of existence and stability of various periodic orbits and of chaos. This knowledge will help in understanding the bifurcation phenomena in a large number of practical systems which can be modeled by discontinuous maps in discrete domain.

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47

HE, DA-REN. "CHARACTERISTICS OF DISCONTINUOUS AND NONINVERTIBLE 2-D MAPS." International Journal of Modern Physics B 21, no. 23n24 (September 30, 2007): 3960–66. http://dx.doi.org/10.1142/s0217979207045025.

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Анотація:

This paper presents a review on recent investigations about the classic dynamics general features of the noninvertible and discontinuous two-dimensional maps. For concreteness we consider a system with phase space divided into two distinct but complementary regions R1 and R2. They are the domains of the map functions f1(x) and f2(x), respectively. The common features of the systems include: the stochastic web formed by image set of discontinuous borderline; phase collapse caused by the irreversibility (quasi-dissipation); fat fractal forbidden web; riddled-like attraction basin and the induced unpredictability of attractors. Several different cases where f1(x) and f2(x) are both area preserving; one is area preserving and another is dissipative; or both are dissipative have been studied. In all the cases the dynamics features can be displayed, however with different characteristics. The features are interesting and can be verified experimentally.

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48

Makrooni, Roya, Neda Abbasi, Mehdi Pourbarat, and Laura Gardini. "Robust unbounded chaotic attractors in 1D discontinuous maps." Chaos, Solitons & Fractals 77 (August 2015): 310–18. http://dx.doi.org/10.1016/j.chaos.2015.06.012.

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HUFF, ROBERT, and JOHN MCCUAN. "MINIMAL GRAPHS WITH DISCONTINUOUS BOUNDARY VALUES." Journal of the Australian Mathematical Society 86, no. 1 (February 2009): 75–95. http://dx.doi.org/10.1017/s1446788708000335.

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Анотація:

AbstractWe construct global solutions of the minimal surface equation over certain smooth annular domains and over the domain exterior to certain smooth simple closed curves. Each resulting minimal graph has an isolated jump discontinuity on the inner boundary component which, at least in some cases, is shown to have nonvanishing curvature.

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50

Joshi, Divya D., Prashant M. Gade, and Sachin Bhalekar. "Study of low-dimensional nonlinear fractional difference equations of complex order." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 11 (November 2022): 113101. http://dx.doi.org/10.1063/5.0095939.

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Анотація:

We study the fractional maps of complex order, [Formula: see text], for [Formula: see text] and [Formula: see text] in one and two dimensions. In two dimensions, we study Hénon, Duffing, and Lozi maps, and in [Formula: see text], we study logistic, tent, Gauss, circle, and Bernoulli maps. The generalization in [Formula: see text] can be done in two different ways, which are not equivalent for fractional order and lead to different bifurcation diagrams. We observed that the smooth maps, such as logistic, Gauss, Duffing, and Hénon maps, do not show chaos, while discontinuous maps, such as Bernoulli and circle maps,show chaos. The tent and Lozi map are continuous but not differentiable, and they show chaos as well. In [Formula: see text], we find that the complex fractional-order maps that show chaos also show multistability. Thus, it can be inferred that the smooth maps of complex fractional order tend to show more regular behavior than the discontinuous or non-differentiable maps.

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